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Topological degree method for the rotationally symmetric $L_p$-Minkowski problem

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  • Consider the existence of rotationally symmetric solutions to the $L_p$-Minkowski problem for $p=-n-1$. Recently a sufficient condition was obtained for the existence via the variational method and a blow-up analysis in [16]. In this paper we use a topological degree method to prove the same existence and show the result holds under a similar complementary sufficient condition. Moreover, by this degree method, we obtain the existence result in a perturbation case.
    Mathematics Subject Classification: Primary: 35J96, 35J75, 53A15; Secondary: 34C40.


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